Abstract : In this paper we provide a comprehensive analysis of the Bovine spongiform encephalopathy BSE epidemic evolution in Great-Britain. Our study is based on a multi-type branching process model and on different stochastic and statistical tools. We first focus on the growth phase until the first sanitary control measure in 1988, and provide an estimation of the unknown parameters of our model, using a Bayesian approach. We then consider the decay phase of the epidemic and estimate its new infection parameter using a frequentist approach, which enables us to predict the future incidences of cases, the epidemic extinction time and the total epidemic size. We finally evaluate the risks that would be caused by a very long decay phase. For this purpose we condition the process on a very late extinction, and thanks to an estimation of the infection parameter, we predict the evolution of the epidemic in this worst-case scenario.